Parametric Trend Estimation

This example shows how to estimate nonseasonal and seasonal trend components using parametric models. The time series is monthly accidental deaths in the U.S. from 1973 to 1978 (Brockwell and Davis, 2002).

Step 2: Fit Quadratic Trend

Step 3. Detrend Original Series.

Subtract the fitted quadratic line from the original data.

xt = y - tH;

Step 4. Estimate Seasonal Indicator Variables

Create indicator (dummy) variables for each month. The first indicator is equal to one for January observations, and zero otherwise. The second indicator is equal to one for February observations, and zero otherwise. A total of 12 indicator variables are created for the 12 months. Regress the detrended series against the seasonal indicators.

In this regression, all 12 seasonal indicators are included in the design matrix. To prevent collinearity, an intercept term is not included (alternatively, you can include 11 indicators and an intercept term).